Simplify the following expression: $z = \dfrac{-48t - 56}{-8t + 40}$ You can assume $t \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-48t - 56 = - (2\cdot2\cdot2\cdot2\cdot3 \cdot t) - (2\cdot2\cdot2\cdot7)$ The denominator can be factored: $-8t + 40 = - (2\cdot2\cdot2 \cdot t) + (2\cdot2\cdot2\cdot5)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $z = \dfrac{(8)(-6t - 7)}{(8)(-t + 5)}$ Dividing both the numerator and denominator by $8$ gives: $z = \dfrac{-6t - 7}{-t + 5}$